The Harnack inequality for a class of degenerate elliptic operators

2011/12/14 by François Hamel, Francois Hamel, Hamel, Francois +3
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1112.3200

arxiv created 2011/12/14 · openalex publication_date 2011/12/14 · arxiv updated 2011/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a Harnack inequality for distributional solutions to a type of degenerate elliptic PDEs in N dimensions. The differential operators in question are related to the Kolmogorov operator, made up of the Laplacian in the last N-1 variables, a first-order term corresponding to a shear flow in the direction of the first variable, and a bounded measurable potential term. The first-order coefficient is a smooth function of the last N-1 variables and its derivatives up to certain order do not vanish simultaneously at any point, making the operators in question hypoelliptic.

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